Microwave photons emitted from opposite sides of the sky appear to be in
thermal equilibrium at almost the same temperature. The most natural
explanation for this is that the Universe has indeed reached a state of
thermal equilibrium, through interactions between the different regions.
But unfortunately in the big bang theory this is not possible.
There was no time
for those regions to interact before the photons were emitted, because of
the finite horizon size,

(25)

This says that the distance light could travel before the microwave
background was released is much smaller than the present horizon distance.
In fact, any regions separated by more than about 2 degrees would be
causally separated at decoupling in the hot big bang theory. In the big
bang theory there is therefore no explanation of why the Universe
appears so homogeneous.

In more recent years this problem has been brought into sharper focus
through the improving understanding of irregularities in the Universe,
as will be discussed later in this article. The same argument that
prevents the smoothing of the Universe also prevents the creation of
irregularities. For example, as we will see the COBE satellite observes
irregularities on all accessible angular scales, from a few degrees
upwards. In the simplest cosmological models, where these
irregularities are intrinsic to the last scattering surface, the
perturbations are on too large a scale to have been created between the
big bang and the time of decoupling, because the horizon size at
decoupling subtends only a degree or so. Hence these perturbations must
have been part of the initial conditions.
(2)

If this is the case, then the hot big bang theory does not allow a
predictive theory for the origin of structure. While there is no reason
why it is required to give a predictive theory, this would be a major
setback and disappointment for the study of structure formation in the
Universe.

2 Note though that it
is not yet known for definite that there are large-angle perturbations
intrinsic to the last scattering surface. For example, in a topological
defect model such as cosmic strings, such perturbations could be
generated as the microwave photons propagate towards us.
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